Method of processing a workpiece by controlling a set of plasma parameters through a set of chamber parameters using surfaces of constant value

ABSTRACT

A workpiece is processed on a workpiece support pedestal in a plasma reactor chamber in accordance with user-selected values of plural plasma parameters of a group comprising ion density, wafer voltage, etch rate, wafer current, by controlling the chamber parameters of source power and bias power. The method includes the following steps: (a.) for each one of the plural plasma parameters, fetching from a memory a relevant surface of constant value corresponding to the user-selected value of the one plasma parameter, the surface being defined in a space of which each of the chamber parameters is a dimension, and determining an intersection of the relevant surfaces, the intersection corresponding to a target value of source power and bias power; and (b.) setting the source power and bias power, respectively, to the target values. In preparation for the foregoing steps, a set of surfaces of constant value for each of the plasma parameters is stored in the memory, the set of surfaces corresponding to a set of constant values spanning a predetermined value range of the corresponding plasma parameter.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.10/440,364, filed May 16, 2003 by Daniel Hoffman, entitled PLASMADENSITY, ENERGY AND ETCH RATE MEASUREMENTS AT BIAS POWER INPUT AND REALTIME FEEDBACK CONTROL OF PLASMA SOURCE AND BIAS POWER and assigned tothe present assignee.

BACKGROUND OF THE INVENTION

Plasma reactors employed in microelectronic circuit fabrication can etchor deposit thin film layers on a semiconductor substrate. In a plasmareactive ion etch process, the etch rate, ion density, wafer voltage andwafer current are critical in controlling etch selectivity, waferheating, etch striations, ion bombardment damage, etch stopping, featuresize and other effects. Such control becomes more critical as featuresize decreases and device density increases. The main problem is thatpresent techniques for measuring etch rate, ion density, wafer voltageand wafer current tend to be highly inaccurate (in the case of the wafervoltage) or must be performed by examining a test workpiece or wafer atthe conclusion of processing (in the case of etch rate). There appearsto be no accurate technique for measuring these parameters in “realtime” (i.e., during wafer processing). As a result, the plasma reactorcontrol parameters (source power, bias power, chamber pressure, gas flowrate and the like) must be selected before processing a currentworkpiece based upon prior results obtained by processing otherworkpieces in the chamber. Once target values for each of the reactorcontrol parameters have been chosen to achieve a desired etch rate or adesired wafer voltage or a desired ion density, the target values mustremain the same throughout the process step, and all efforts arededicated to maintaining the chosen target values. If for example thechosen target value of one of the control parameters unexpectedly leadsto a deviation from the desired processing parameter (e.g., etch rate),this error will not be discovered until after the current workpiece hasbeen processed and then examined, and therefore the current workpiece orwafer cannot be saved from this error. As a result, the industry istypically plagued with significant losses in material and time.

A related problem is that plasma process evolution and design is slowand inefficient in that the discovery of optimal target values for thereactor control parameters of source power, bias power, chamber pressureand the like typically relies upon protracted trial and error methods.The selection of target values for the many reactor control parameters(e.g., source power, bias power, chamber pressure and the like) toachieve a particular etch rate at a particular wafer current (to controlwafer heating) and at a particular wafer voltage (to control ionbombardment damage) and at a particular ion density (to control etchselectivity, for example) is a multi-dimensional problem. The mutualdependence or lack thereof among the various reactor control parameters(source power, bias power, chamber pressure, etc.) in reaching thedesired target values of the process parameters (e.g., etch rate, wafervoltage, wafer current, ion density) is generally unknown, and the trialand error process to find the best target values for the reactor controlparameters (bias and source power levels and chamber pressure) isnecessarily complex and time consuming. Therefore, it is not possible tooptimize or alter target values for the process parameters (e.g., etchrate, etc.) without a time-consuming trial and error process. Thus,real-time plasma process control or management has not seemed possible.

SUMMARY OF THE INVENTION

A workpiece is processed on a workpiece support pedestal in a plasmareactor chamber in accordance with user-selected values of plural plasmaparameters of a group comprising ion density, wafer voltage, etch rate,wafer current, by controlling the chamber parameters of source power andbias power. The method includes the following steps: (a.) for each oneof the plural plasma parameters, fetching from a memory a relevantsurface of constant value corresponding to the user-selected value ofthe one plasma parameter, the surface being defined in a space of whicheach of the chamber parameters is a dimension, and determining anintersection of the relevant surfaces, the intersection corresponding toa target value of source power and bias power; and (b.) setting thesource power and bias power, respectively, to the target values. Inpreparation for the foregoing steps, a set of surfaces of constant valuefor each of the plasma parameters is stored in the memory, the set ofsurfaces corresponding to a set of constant values spanning apredetermined value range of the corresponding plasma parameter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a plasma reactor and a measurement instrumenttherefor.

FIG. 2 illustrates an electrical model of the plasma reactor employed bythe measurement instrument.

FIG. 3 illustrates the structure of the measurement instrument of FIG.1.

FIG. 4 illustrates an input phase processor of the measurementinstrument of FIG. 3.

FIG. 5 illustrates a transmission line transformation processor in themeasurement instrument of FIG. 3.

FIG. 6 illustrates a grid-to-ground transformation processor in themeasurement instrument of FIG. 3.

FIG. 7 illustrates a grid-to-wafer transformation processor in themeasurement instrument of FIG. 3.

FIG. 8 illustrates a combined transformation processor in themeasurement instrument of FIG. 3.

FIG. 9 illustrates a process feedback control system for a plasmareactor that includes the measurement instrument of FIG. 3.

FIG. 10 illustrates an alternative implementation of the processfeedback control system.

FIG. 11 illustrates the measurement instrument of FIG. 3, a constantcontour generator and a process set point controller connected in asystem with a plasma reactor.

FIGS. 12, 13 and 14 illustrate different contours of constantperformance parameter values produced by the system of FIG. 11.

FIG. 15 illustrates a method of finding an optimal operating point atthe intersection of different contours of constant parameter values.

FIG. 16 illustrates the process set point controller in the system ofFIG. 11.

FIGS. 17, 18 and 19 illustrate respective operations performed by theprocess set point controller of the contour generator in the system ofFIG. 11.

FIG. 20 illustrates an overlay of contours of constant wafer voltage,contours of constant etch rate and contours of constant ion density at achamber pressure of 100 mT.

FIG. 21 illustrates an overlay of contours of constant wafer voltage,contours of constant etch rate and contours of constant ion density at achamber pressure of 30 mT.

FIG. 22 illustrates an overlay of contours of constant wafer voltage,contours of constant etch rate and contours of constant ion density at achamber pressure of 70 mT.

FIG. 23 illustrates an overlay of contours of constant wafer voltage,contours of constant etch rate and contours of constant ion density at achamber pressure of 150 mT.

FIG. 24 illustrates an overlay of contours of constant wafer voltage,contours of constant etch rate and contours of constant ion density at achamber pressure of 200 mT.

FIG. 25 illustrates an overlay of contours of constant wafer voltage,contours of constant etch rate and contours of constant ion density at achamber pressure of 250 mT.

DETAILED DESCRIPTION OF THE INVENTION

Introduction:

The present description pertains to a plasma reactor having a plasmasource power applicator (such as an overhead electrode or antenna) inwhich plasma bias power is applied to the wafer through the wafersupport pedestal. I have discovered a measurement instrument (describedbelow) that is the first one known to instantaneously and accuratelymeasure wafer voltage, wafer current, ion density and etch rate. Themeasurement instrument uses only conventional electrical sensors at thebias power input that sense voltage, current and power at the output ofan impedance match device coupled to the wafer support pedestal. Themeasurement instrument is therefore non-invasive of the plasma etchprocess occurring within the reactor chamber in addition to beingaccurate. The degree of accuracy is surprising, surpassing even the bestknown instruments and measurement techniques currently in use.

I have invented a plasma reactor having a feedback controller employingthis same measurement instrument, in which plasma source power andplasma bias power are controlled in separate feedback control loops. Inthe bias power feedback control loop, plasma bias power is served orcontrolled to minimize the difference between a user-selected targetvalue of the ion energy (or, equivalently, wafer voltage) and the actualion energy sensed in real time by my measurement instrument.Simultaneously, in the source power feedback control loop, plasma sourcepower is served or controlled to minimize the difference between auser-selected target value of the plasma ion density and the actualplasma ion density sensed in real time by my measurement instrument anda user-selected target value for the ion density. One surprising featureof my feedback controller is that a measurement at the bias power inputis used to control the source power.

In addition, I have solved the problem of how to select the targetvalues for ion density and ion energy. Because my measurement instrumentprovides instantaneous, accurate and simultaneous measurements ofperformance parameters such as wafer voltage (or, equivalently, ionenergy), wafer current, ion density and etch rate, it has enabled me toobserve accurately, for the first time, the real-time behavior of allthese performance parameters simultaneously as a function of controlparameters such as plasma source power, plasma bias power and others(e.g., chamber pressure, source power frequency, applied magnetic field,etc.). These observations have led to my discovery herein that thecontrol parameters of plasma source power level and plasma bias powerlevel affect the set of performance parameters (e.g., etch rate, ionenergy, ion density) in the manner of a pair of independent variables.This discovery greatly simplifies the task of controlling plasmaprocessing: by holding various other control parameters constant duringprocessing (i.e., constant chamber pressure, constant gas flow rates,constant source power frequency and bias power frequency, etc.), theprocess is controlled entirely through the bias and source power levels.I have used this technique to parameterize all of the performanceparameters (including etch rate, ion energy and others) as uniquefunctions of two independent variables, namely source power level andbias power level. From this, I have generated curves in 2-dimensionalsource power-bias power space of constant etch rate, constant ion energyand constant ion density, for example. A process controller responds touser-selected ranges for the various performance parameters (etch rate,ion energy, ion density) using the curves of constant etch rate,constant ion density and constant ion energy to instantaneously find atarget value for the source power level and the bias power level. Thisprocess controller provides the target values for the plasma sourcepower level and plasma bias power level to the feedback controllerreferred to above.

As a result, a user need not have any knowledge of the controlparameters (e.g., bias and source power levels) that may be required torealize a desired set of performance parameter values (e.g., etch rate)nor a corresponding understanding of the reactor's behavior in thisregard. Instead, the user merely inputs to the control processor his setof desired performance parameter values or ranges, and the controlprocessor instantly specifies target control parameter values (targetsource power and bias power values) to the feedback controller referredto above. Thereafter, control of the plasma process is entirelyautomatic, and can instantly accommodate any changes the user mayintroduce. For example, the user may specify different etch rates atdifferent times during the same etch step, so that one etch rateprevails during the beginning of an etch process and another prevailstoward the end of the process, for example. The user need not specifyany control parameters, but only the results he desires (i.e., theperformance parameters such as etch rate, etc.).

Instrument for Instantaneously Measuring Performance ParametersIncluding Etch Rate, Ion Density and Ion Energy:

Referring to FIG. 1, a plasma reactor 100 has a chamber enclosure 105enclosing a vacuum chamber 110 in which a wafer support pedestal 115supports a semiconductor wafer 120 being processed. Plasma RF bias powerfrom an RF bias power generator 125 is applied through an impedancematch circuit 130 to the wafer support pedestal 115. Conventionalsensing circuits 132 within the impedance match circuit 130 have threeoutput terminals 132 a, 132 b, 132 c providing respective signalsindicating the power (P_(bias)), voltage (V) and current (I) furnishedat the output of the impedance match circuit 130 to the wafer supportpedestal 115. A measurement instrument 140, which is the measurementinstrument referred to above in this specification, uses the signalsfrom the output terminals 132 a, 132 b, 132 c to measure,simultaneously, etch rate on the wafer 120, ion energy at the wafersurface (or equivalently, wafer voltage), ion density in the reactorchamber and electric current through the wafer 120. The measurementinstrument 140 employs processes based upon an electrical model of thereactor 100. This model is illustrated in FIG. 2.

FIG. 2 depicts the plasma reactor of FIG. 1 in greater detail, so thatthe individual elements of the wafer support pedestal 115 are visible,including an electrode 115-1, a thin overlying dielectric (e.g.,ceramic) layer 115-2, an underlying dielectric (e.g., ceramic) layer115-3, and a conductive (e.g., aluminum) planar ground plate 115-4 atthe bottom of the pedestal 115. The electrode 115-1 takes the form of aconductive grid in the illustrated embodiment, and may be implemented invarious forms such as a conductive solid plate or as a conductive mesh,for example. While the electrode 115-1 will hereinafter be referred toas a conductive grid, the term “grid” as employed in this specificationrefers to all forms that the electrode 115-1 may take, such as aconductive solid plate, or a conductive mesh, or a conductive screen, ora form combining aspects of any or all of the foregoing forms, forexample. Also visible in FIG. 2 is a coaxial cable 210 connecting theoutput of the impedance match circuit 130 to the grid 115-1. The coaxialcable 210 has an inner conductor 212 and an outer conductor 214. Anelectrical model with parameters depicted in FIG. 2 characterizes theelectrical properties of the plasma reactor 100, which are readilydetermined using conventional techniques. Specifically, the coaxialtransmission line or cable 210 is characterized by three quantities: (1)its length, (2) Z_(ch), its characteristic impedance, and (3) V_(ch),its complex phase velocity in the transmission line equation. The wafersupport pedestal 115 is characterized by electrical properties of theoverlying and underlying dielectric layers 115-2 and 115-3.Specifically, the underlying dielectric layer 115-3 has a capacitanceCD, which is a function of (1) the dielectric constant, ED, of thedielectric layer 115-3, and (2) the conductive loss component of thedielectric layer 115-3, tan_(D), (3) the thickness, gap, of thedielectric layer 115-3 and (4) the radius of the wafer 120. Theoverlying dielectric layer 115-2 has a capacitance C_(P) which is afunction of (1) the thickness, gap_(P), of the dielectric layer 115-2,(2) the dielectric constant, ε_(P), of the dielectric layer 115-2 and(3) the conductive loss component of the dielectric layer 115-2,tan_(P). The plasma 220 is characterized by an admittance Y_(plasma) (toRF ground such as the interior chamber walls or ceiling) that consistsof a real part (the conductance g) and an imaginary part (thesusceptance b). Each of these electrical parameters has a role in theoperation of the measurement instrument 140.

FIG. 3 illustrates the structure of the measurement instrument 140 ofFIG. 1. An input phase processor 310 receives the P_(bias,) V and Isignals from the impedance match sensing circuit 132 of FIG. 1 andproduces respective signals indicating a complex impedance Z, a complexinput current I_(in) and a complex input voltage V_(in) at the near endof the coaxial cable 210 (i.e., the end nearest the impedance matchcircuit 130). A transmission line transformation processor 320 uses thecharacteristic impedance Z_(ch) and the complex loss coefficient V_(ch)(in the transmission line equation) from an electrical model 330 of thecoaxial cable 210 to transform from Z, I_(in) and V_(in) at the nearcable end to an admittance Y_(junction) at the far cable end, i.e.,atthe junction between the coaxial cable 210 and the grid 115-1. Agrid-to-ground transformation processor 340 takes radius, gap, ε_(D) andtan_(D) from a model 345 of the grid-to-ground capacitance and producesa dielectric resistance R_(D) and dielectric capacitance C_(D). Agrid-to-wafer transformation processor 350 takes radius, gap_(P), ε_(P)and tan_(P) from a model 355 of the grid-to-wafer capacitance andproduces a plasma resistance R_(P) and a plasma capacitance C_(P). Acombined transformation processor 360 accepts the outputs of all theother processors 320, 340, 350 and computes the admittance Y_(plasma)through the plasma from the wafer to RF ground and computes the wafervoltage V_(wafer) (or ion energy) . From the plasma admittance and fromthe wafer voltage, the following quantities are computed: wafer currentI_(wafer), the etch rate and the ion density.

In summary, electrical measurements are made at the output of theimpedance match circuit 130. The transmission line transformationprocessor 320 transforms these measurements at the near end of the cable210 to an admittance at the far end. The grid to ground transformationprocessor 340 provides the transformation from the ground plane 115-4near the far end of the cable to the conductive grid 115-1. Thegrid-to-wafer transformation processor 350 provides the transformationfrom the conductive grid 115-2 to the wafer 120. Using all of theforegoing transformations, the combined transformation processor 360provides the transformation across the plasma in the form of the plasmaadmittance. From the plasma admittance, various performance parameterssuch as etch rate and plasma ion density are computed.

The transmission line model 330, the model of the grid-to-groundcapacitance 345 and the model 355 of the grid-to-wafer capacitance arenot necessarily a part of the measurement instrument 140. Or, they maybe memories within the measurement instrument 140 that store,respectively, the coaxial cable parameters (V_(ch) and Z_(ch)), thegrid-to-ground capacitance parameters (gap, ε_(D), tan_(D) and radius)and the grid-to-wafer capacitance parameters (gap_(P), ε_(P), tan_(P)and radius).

FIG. 4 illustrates the structure of the input phase processor 310 ofFIG. 3. A delivered power arithmetic logic unit (ALU) 410 computesdelivered power P from the outputs I and P_(bias) from the impedancematch sensing circuit 132 as P_(bias)−(0.15)I². A phase angle ALU 420computes phase angle θ from the delivered power P and from V and I ascos⁻¹ (P/VHI) . An impedance ALU 430 computes the complex impedance Z as(V/I)e^(iθ) , where i=(−1)^(1/2). An input current ALU 440 computes theinput current I_(in) to the coaxial cable 210 as [P/Re(Z)]^(1/2). Aninput voltage ALU 450 computes the input voltage V_(in) to the coaxialcable 210 as ZHI_(in).

FIG. 5 illustrates the structure of the transmission line transformationprocessor 320 of FIG. 3. The transmission line processor receives I_(in)and V_(in) as inputs from the input phase processor 310 of FIG. 4 anduses the transmission line model parameters V_(ch) and Z_(ch) (from thetransmission line model or memory 330 of FIG. 3) to compute theadmittance Y_(junction) as follows: A junction current ALU 510 computesthe current I_(junction) at the junction of the coaxial cable 210 andthe grid 115-1 (FIG. 1) as:(I _(in))cosh[(V _(ch))(−length)]+(V _(in) /Z _(ch))sinh[(V_(ch))(−length)].

A junction voltage ALU 520 computes the voltage V_(junction) at thejunction between the coaxial cable 210 and the grid 115-1 as:(V _(in))cosh[(V _(ch))(−length)]+(I _(in)Z_(ch))sinh[(V_(ch))(−length)].

A divider 530 receives I_(junction) and V_(junction) computesY_(junction) as I_(junction)/V_(junction). It should be noted that eachof the electrical quantities in the foregoing computations (current,voltage, impedance, admittance, etc.) is a complex number having both areal part and an imaginary part.

FIG. 6 illustrates the structure of the grid-to-ground transformationprocessor 340 of FIG. 3. The grid-to-ground transformation processor 340receives the parameters gap, ε_(D), tan_(D) and rad (the wafer radius)from the grid-to-ground model or memory 345 of FIG. 3 computes thedielectric resistance R_(D) and the dielectric capacitance C_(D). Thedielectric capacitance C_(D) is computed by a CD ALU 610 as follows:(ε_(D))(ε_(D))π(rad)²/gapwhere ε_(O) is the electrical permittivity of free space. An RD ALU 620uses the value of C_(D) from the CD ALU 610 and computes the dielectricresistance R_(D) as follows:(tan_(D))/(ω C _(D) gap²)

where ω is the angular frequency of the bias RF generator 125 of FIG. 2.

FIG. 7 illustrates the structure of the grid-to-wafer transformationprocessor 350 of FIG. 3. The grid-to wafer transformation processor 350receives the parameters gap_(P), ε_(P), tan_(P) and rad from thegrid-to-wafer model or memory 355 of FIG. 3 and computes the plasmaresistance R_(P) and the plasma capacitance C_(P). The plasmacapacitance C_(P) is computed by a CP ALU 710 as follows:(ε_(O))(ε_(P))π(rad)²/gap_(P)where ε_(O) is the electrical permittivity of free space. An RP ALU 720uses the value of C_(P) from the CP ALU 710 and computes the plasmaresistance R_(P) as follows:(tan_(P))/(ω C _(P) gap_(C) ²)where ω is the angular frequency of the bias RF generator 125 of FIG. 2.

FIG. 8 illustrates the structure of the combined transformationprocessor 360 of FIG. 3. The combined transformation processor 360receives the parameters R_(D), C_(D) from the processor 340 of FIG. 3,receives the parameters R_(P), C_(P) from the processor 350 of FIG. 3and receives the parameter Y_(junction) from the processor 320 of FIG.3. A grid impedance ALU 810 computes Z_(grid) (the impedance at the grid115-1 of FIG. 2) as follows:[Y _(junction)−1/(R _(D)+(1/(iωC _(D))))]⁻¹

A wafer impedance ALU 820 uses the output of the grid impedance ALU 810to compute Z_(wafer) (the impedance at the wafer 120 of FIG. 2) asfollows:Z _(grid)−1/(R_(P)+(1/(iωC _(P))))

A wafer voltage ALU 830 uses the outputs of both ALU=s 810 and 820 andV_(junction) from the divider 530 of FIG. 5 to compute the voltage onthe wafer 120 of FIG. 2, V_(wafer), as V_(junction) Z_(wafer)/Z_(grid).A wafer current ALU 840 uses the outputs of the ALU=s 820 and 830 tocompute the wafer current I_(wafer) as V_(wafer)/Z_(wafer). Anadmittance ALU 850 uses the output of the ALU 820 to compute theadmittance of the plasma, Y_(plasma), as 1/Z_(wafer). A susceptance ALU860 uses the output of the ALU 850 to compute the plasma susceptance, b,as Im(Y_(plasma)) . An etch rate ALU 870 uses the wafer voltage from theALU 830 and the susceptance from the ALU 860 to compute the etch rate asb² V_(wafer) ². An ion density ALU 880 uses the same outputs to computethe ion density as kb² V_(wafer) ^(3/2), where k is a constant given by:(2^(3/2)/3²)(1/[qε_(O)A²π²f²T_(e) ²])where q is the electron charge, A is the area of the wafer 120 of FIG.2, f is the frequency of the bias power generator 125 of FIG. 2 andT_(e) is the electron temperature in volts. This relationship betweenion density and the measured quantities b and V_(wafer) follows from anapproximate formula for the plasma susceptance and a formula for theplasma sheath thickness. The plasma susceptance may be approximated asεAω/γ, where ε is the electrical permittivity within the plasma, A isthe electrode area, ω is the angular frequency of the bias power signaland γ is the plasma sheath thickness. The plasma sheath thickness may beapproximated as [T_(e)/(qη)]^(1/2)[2V_(wafer)/T_(e)]^(3/4), where T_(e)is electron temperature, q is the electron charge and η is ion density.Substituting the expression for sheath thickness into the expression forthe susceptance and solving for ion density yields an expression for iondensity as a function of susceptance and wafer voltage.Process Feedback Control System:

FIG. 9 illustrates a process feedback control system that uses themeasurement instrument 140 of FIG. 3. A plasma reactor 900 includes allof the features of the plasma reactor 100 of FIG. 1, and in additionincludes an overhead RF source power applicator 910 connected through animpedance match circuit 915 to an RF source power generator 920. The RFsource power applicator 910 may be, for example, a ceiling electrodethat is insulated from the grounded chamber enclosure 105. The powerlevel of the RF plasma source power generator 920 generally controls theplasma ion density while the power level of the RF plasma bias powergenerator 125 generally controls the ion energy at the wafer surface.The measurement instrument 140 receives the power, voltage and currentoutputs from the sensor circuit 132 of the impedance match circuit 130.From these quantities, the measurement instrument 140 computes theplasma susceptance b and computes the wafer voltage V_(wafer), which isoutput as a measurement signal. These computations are carried out inthe manner described above with reference to FIG. 5. The measurementinstrument 140 can then compute the ion density and/or the etch ratefrom b and V_(wafer), in the manner described above with reference toFIG. 5. At least two of the three measurement signals thus produced bythe measurement instrument 140 can be used in a feedback control loop.

A feedback controller 950 uses the measurement signals from themeasurement instrument 140 to create feedback signals to control thepower level of the RF plasma bias power generator 125 and the powerlevel of the RF plasma source power generator 920. The ion energy at thewafer surface, which is equivalent to the wafer voltage V_(wafer), isdirectly controlled by the power level of the bias power generator 125.Therefore, the wafer voltage measurement signal from the measurementinstrument 140 (i.e., V_(wafer) from the ALU 830 of FIG. 8) is used bythe feedback controller 950 to control the bias power generator 125 in abias power feedback control loop 957. The source power generator 920, onthe other hand, directly controls plasma ion density. Therefore, plasmaion density measurement signal from the measurement instrument 140(i.e., kb²V_(wafer) ^(3/2) from the ALU 880 of FIG. 8) is used by thefeedback controller 950 to control the source power generator 920 in asource power feedback control loop 958.

The bias power feedback control loop 957 includes a memory 960 thatstores a selected or desired target value of the wafer voltage or ionenergy, [V_(wafer)]_(TARGET). A subtractor 962 subtracts this targetvalue from the sensed wafer voltage V_(wafer) to produce an errorsignal. The gain of the bias power feedback loop 957 is determined by abias power feedback gain factor stored in a memory 964. A multiplier 966multiplies the error signal from the subtractor 962 by the gain factorin the memory 964 to produce a correction signal used to control thepower level of the bias power generator 125. The path of the bias powerfeedback control loop 957 is completed by the V, I and P_(bias) signalsapplied to the measurement instrument 140 to produce the measurementsignal V_(wafer) representing the wafer voltage.

The source power feedback control loop receives from the measurementinstrument 140 the sensed ion density value b²V_(wafer) ^(3/2). A memory975 stores a selected or desired target value of the ion density,[b²V_(wafer) ^(3/2)]_(TARGET). A subtractor 980 computes the differencebetween the measured ion density and the ion density target value toproduce an error signal. The gain of the source power feedback controlloop 958 is determined by a source power feedback gain factor stored ina memory 985. A multiplier 990 multiplies the error signal from thesubtractor 980 by the gain factor from the memory 985 to produce acorrection signal. This correction signal is used to control the powerlevel of the RF source power generator 920. The path of the source powerfeedback control loop 958 is completed by the V, I and P_(bias) signalsapplied to the measurement instrument 140 to produce the measurementsignal b²V_(wafer) ^(3/2) representing the ion density.

At the start of a plasma process step such as an etch process step,initial values for the power levels P_(S) and P_(B) of the RF sourcepower generator 920 and the RF bias power generator 125, respectively,can be specified. If these initial values are sufficiently close to theoptimum values, this feature can avoid unduly large initial correctionsby the feedback controller 950. For this purpose, the bias powerfeedback loop 957 includes a bias power command processor 992 coupled toreceive the feedback correction signal from the multiplier 957 and toreceive a target value for the bias power, [P_(bias)]_(TARGET). Beforeplasma processing begins, there is no feedback signal, and the biaspower command processor 992 sets the power level of the bias powergenerator 125 to the initial target value [P_(bias)]_(TARGET). Onceprocessing begins and a feedback signal is present, the bias powercommand processor 992 controls the bias power in accordance with thefeedback correction signal from the multiplier 966 rather than the biaspower target value.

Similarly, the source power feedback loop 958 includes a source powercommand processor 994 coupled to receive the feedback correction signalfrom the multiplier 990 and to receive a target value for the sourcepower, [P_(source)]_(TARGET). Before plasma processing begins, there isno feedback signal, and the source power command processor 994 sets thepower level of the source power generator 920 to the initial targetvalue [P_(source)]_(TARGET). Once processing begins and a feedbacksignal is present, the source power command processor 994 controls thesource power in accordance with the feedback correction signal from themultiplier 990 rather than the source power target value.

In accordance with another aspect, the source and bias power commandprocessors 992, 994 can be instructed by the user to ignore theirrespective feedback control loops 957, 958 throughout much or all of theprocess step and instead maintain the source and bias power levels atthe specified target values [P_(source)]_(TARGET) and[P_(bias)]_(TARGET). The user can change these values from time to timeduring processing.

Referring to FIG. 10, the feedback control processor 950 may employ theetch rate rather than the ion density as the measured parameter in thesource power feedback control loop 958. In the measurement instrument140, the etch rate measurement signal is taken from the ALU 870 of FIG.8 that computes b²V_(wafer) ². In FIG. 10, a memory 975' (in lieu of thememory 975 of FIG. 9) stores a target value of the etch rate,[b²V_(wafer) ^(2]) _(TARGET). The subtractor 980 operates as describedwith reference to FIG. 9 to produce an error signal. The remainder ofthe source power feedback control loop of FIG. 10 generally is the sameas in FIG. 9.

Process Set Point Controller:

The feedback controller 950 requires a number of target values forvarious process control parameters. Specifically the feedback controller950 of FIG. 9 has a memory 975 storing the target value for the iondensity, [b²V_(wafer) ^(3/2)]_(TARGET), and a memory 960 storing thetarget value for the ion energy (or, equivalently, wafer voltage),[V_(wafer)]_(TARGET). In the feedback controller of FIG. 10, the memory975 is replaced by the memory 975' storing the target value for the etchrate, [b²V_(wafer) ²]_(TARGET). In addition, the feedback controller 950can employ initial target values [P_(source)]_(TARGET) and[P_(bias)]_(TARGET) for the source and bias power levels respectively toinitialize the feedback controller 950, as discussed above. Theselection or optimization of these target values can be left to theuser's efforts, which may involve an undue amount of trial and error andmay be unreliable. Typically, a user who wishes to achieve certainprocess results (e.g., a certain etch rate, a certain ion energy, areduction in etch processing artifacts such as striations, a reductionin heating due to wafer current, etc.) must conduct a time-consumingprogram of trial and error experiments to find the optimum processcontrol parameters values to achieve the desired results. For thisreason, the alteration of an existing process or the design of a newprocess must be undertaken over a very long development period.

In order to overcome this limitation, a process set point controller1110 employed in the reactor of FIG. 11 automatically and quickly (orinstantaneously) finds the optimum target values of process controlparameters based upon the user's selection of values for variousperformance parameters. For example, the process set point controller1110 may determine the target values [P_(source)]_(TARGET) and[P_(bias)]_(TARGET) based upon a desired etch rate and/or a desiredwafer voltage or other performance parameter specified by the user.Thus, a new process recipe can be designed nearly instantaneously. Forpresent plasma reactors, this can take place in milliseconds, but couldbe made to be as fast as microseconds if needed.

There are many process control parameters (i.e., characteristics of thereactor under direct user control such as chamber pressure, source andbias power levels, etc.) and many process performance parameters (i.e.,characteristics of the plasma and process not susceptible of directcontrol such as etch rate, ion density, ion energy, wafer current,etc.). A user can specify any one or more of these performanceparameters as an objective for a given process. Any one or group of orall of the control parameters can be used to achieve the desired levelsof the performance parameters chosen by the user. The question iswhether or not the effects of some of the control parameters might bedependent upon others of the control parameters in controlling theperformance parameters chosen by the user. Thus, the problem ofselecting the right set of control parameters to achieve the desiredresults in the chosen performance parameters is complex and thereappears to be no particularly optimum choice.

However, I have discovered that the source power and the bias powercontrol the performance parameters of interest and do so in anindependent manner. That is, source power P_(source) and bias powerP_(bias) are independent variables and may be thought of as orthogonalentities forming a two-dimensional control space in which control of theperformance parameters may be exercised with such versatility that noalteration of the other control parameters is required. This discoverygreatly reduces the problem to only two variables.

Therefore, the following description will concern a control system inwhich the control parameters, with the exception of P_(source) andP_(bias,) are held constant during processing. Thus, process controlparameters including chamber pressure, gas composition, gas flow rate,source power frequency, bias power frequency, etc., are held constant.The source power and bias power levels (P_(source) and P_(bias)) arevaried to achieve desired values in a specified set of performanceparameters (e.g., etch rate and ion density).

The problem of finding target values for the various parameters given aset of user-defined values for a chosen set of performance parameters issolved by the process set point controller 1110 superimposing a set ofconstant parameter contours in the two-dimensional P_(source)-P_(bias)space referred to above. Such constant parameter contours are obtainedfrom a constant parameter contour generator 1120 in FIG. 11. Forexample, contours of constant ion density (FIG. 12), contours ofconstant ion energy or wafer voltage (FIG. 13), and contours of constantetch rate (FIG. 14) are employed. How the constant parameter contourgenerator 1120 produces these contours using the measurement instrument140 will be described later in this specification. The presentdescription concerns their use by the process set point controller 1110.

Referring to FIG. 12, a set of contours of constant plasma ion densityin P_(source)-P_(bias) space for a chamber pressure of 20 mT generallyhave a small negative slope and a small but positive first derivatived(P_(source))/d(P_(bias)). The top-most contour corresponds to aconstant plasma density of 5H10¹⁰ ions/cm³ while the bottom contourcorresponds to 1.5H10¹⁰ ions/cm³. The vertical axis (P_(source)) rangesfrom 0 to 1500 Watts while the horizontal axis (P_(bias)) ranges from2000 to 4500 Watts. Referring to FIG. 13, a set of contours of constantwafer voltage for the same chamber pressure (20 mT) have a positiveslope and range from 600 volts (at the top) to 1800 Volts (at thebottom). Referring to FIG. 14, a set of contours of constant etch rate(in arbitrary units, e.g., where k=1) have a large negative slope.

The process set point controller 1110 determines how to simultaneouslysatisfy user-selected values of ion density, ion energy and etch rate.It does this by finding the intersection in P_(source)-P_(bias) space ofthe corresponding contours of FIGS. 12-14. This intersection indicatesthe optimum target values for source and bias power, namely[P_(source)]_(TARGET) and [P_(bias)]_(TARGET). The problem is somewhatsimpler if the user specifies values for only two performanceparameters. For example, if the user specifies a wafer voltage of 1100Volts and an ion density of 3.5H10¹⁰ ions/cm³, then the correct point inP_(source)-P_(bias) space is found by superimposing the constant wafervoltage contour for 1100 volts from FIG. 12 and the constant densitycontour for 3.5H10¹⁰ ions/cm³ from FIG. 13 and finding theirintersection in P_(source)-P_(bias) space. This procedure is performedby the process set point controller 1110 and is illustrated in FIG. 15in which the two curves intersect in P_(source)-P_(bias) space at thepoint [850 W, 3750 W]. Therefore, in this example the user'srequirements are met by setting the source power level at 850 W andsetting the bias power level at 3750 W. Thus, in this case the targetvalues [P_(source)]_(TARGET) and [P_(bias)]_(TARGET) furnished to thesource power command processor 994 and bias power command processor 992of FIG. 9 are 850 Watts and 3750 Watts, respectively.

It should be noted that this deduction of the target values of sourceand bias power levels may also result in the deduction of a target valuefor other parameters whose values have not been specified or limited bythe user. As an illustration, in the foregoing example, the user has notspecified a particular etch rate. However, a target value for the etchrate satisfying the user-selected values for ion density and energy canbe found by superimposing the contours of FIG. 14 onto FIG. 15 (or viceversa). The point [850 W, 3750 W] lies on the contour of a constant etchrate of 2.101 (in arbitrary units) of FIG. 14, as indicated by the AX@symbol in that drawing. Therefore, if the feedback controller of FIG. 10is employed, then the set point controller 1110 writes an etch ratetarget value of 2.101 in arbitrary units to the memory 975 of FIG. 10.

An advantage of this feature is that the contours of constant voltage,density, etch rate, etc., are characteristic of the reactor andgenerally do not change for given process conditions. They may thereforebe determined by the constant parameter contour generator 1120 prior toprocessing and made available to the process set point controller 1110constantly during use of the reactor, as indicated in FIG. 11. In thisway, a target value for a particular parameter may be found instantly orwhenever required in the manner illustrated in FIG. 15.

In operation, the bias power command processor 992 and the source powercommand processor 994 receive the target values [P_(source)]_(TARGET)and [P_(bias)]_(TARGET) from the process set point controller 1110 andreceive feedback signals from the multipliers 958 and 957 respectively.During system initialization, the feedback signals are ignored, and theprocessors 992, 994 put the power levels of the RF generators 125, 920to the target values [P_(source)]_(TARGET) and [P_(bias)]_(TARGET),respectively. After processing begins, the feedback signals areavailable and the processors 992, 994 can use the feedback control loops957, 958 instead of the target values to control the source power andbias power levels. Alternatively, the power command processors 992, 994may be programmed so that the target values [P_(source)]_(TARGET) and[P_(bias)]_(TARGET) determine the source and bias power levels not onlyat initialization but also during processing, while the feedback loops957, 958 are ignored.

FIG. 11 shows that the user can apply to the process set pointcontroller 1110 any one or a combination of user selected values forperformance parameters, including etch rate, wafer voltage, ion densityand wafer current. In response, the process set point controller 1110uses the appropriate contours from the contour generator 1120 to producenot only source and bias power target values but, in some cases, targetvalues for other parameters not limited or specified by the user, whichmay be a target value for the etch rate, the ion density, the ion energyor the wafer current. These target values are furnished to the feedbackcontroller 950 for use in the manner described previously in thisspecification with reference to FIG. 9.

FIG. 16 illustrates the structure and operation of the process set pointcontroller 1110 of FIG. 11. A first logic unit 1610 receives an etchrate command (if any) from the user and fetches from a memory 1615 thecorresponding contour of constant etch rate in the set of contours ofconstant etch rates previously generated by the contour generator 1120.A second logic unit 1620 receives an ion density command (if any) fromthe user and fetches from a memory 1625 the corresponding contour ofconstant ion density in the set of contours of constant ion densitypreviously generated by the contour generator 1120. A third logic unit1630 receives a wafer voltage (ion energy) command (if any) from theuser and fetches from a memory 1635 the corresponding contour ofconstant wafer voltage in the set of contours of constant wafer voltagepreviously generated by the contour generator 1120. A fourth logic unit1640 finds the intersection point in P_(source)-P_(bias) space betweenany of the contours selected by the logic units 1610, 1620, 1630. Thisintersection point is output to the feedback controller 950 of FIG. 11as [P_(source)]_(TARGET), [P_(bias)]_(TARGET).

Contour Generator 1120:

Operation of the contour generator 1120 of FIG. 11 is illustrated inFIGS. 17, 18 and 19. FIG. 17 illustrates the operation of the contourgenerator 1120 in finding functions defining how certain performanceparameters vary with bias power. These include functions for theperformance parameters of wafer voltage, ion density and etch rate. Aswill be described below, the observations of changes in wafer voltage,ion density and etch rate with bias power are made for the contourgenerator 1120 by the measurement instrument 140 using the configurationof FIG. 11. In FIG. 11, the measurement instrument 140 transmitsinstantaneous measurements of wafer voltage, ion density and etch rateto the contour generator 1120. The contour generator 1120 also receivesthe current source power and bias power commands, as indicated in FIG.11, allowing it to correlate behavior of the performance parameters ofwafer voltage, ion density and etch rate, with the control parameters ofsource power and bias power.

FIG. 18 illustrates the operation of the contour generator 1120 infinding functions defining how certain performance parameters vary withsource power. As in FIG. 17, in FIG. 18 these include functions for theperformance parameters of wafer voltage, ion density and etch rate. Alsoas in FIG. 17, in the operation of FIG. 18 is carried out using theconfiguration of FIG. 11.

FIG. 19 illustrates the operation of the contour generator 1120 inparameterizing the separate functions of source power and bias powerdiscovered in the operations of FIGS. 17 and 18 into combined functionsof both source power and bias power. Such combined functions representthe behavior of the performance parameters (wafer voltage, ion density,etch rate) in 2-dimensional P_(source)-P_(bias) space. The contourgenerator 1120 then derives the contours of constant ion density, ionenergy and etch rate from the respective combined functions.

The operation depicted in FIG. 17 will now be described in detail withreference to both FIGS. 11 and 17. In the step of block 1710 of FIG. 17,the frequencies of the bias and source power generators 125, 920 of FIG.11 are set to constant values, the exhaust rate of a vacuum pump 1180 ofthe reactor of FIG. 11 is controlled to achieve a constant chamberpressure, and mass flow rates from gas supplies 1182, 1184 are setthrough a mass flow controller 1186 of FIG. 11 to constant values. Inthe step of block 1720 of FIG. 17, the power level of the source powergenerator 920 of FIG. 11 is set to an initial set point, so that theentire process is at a steady state with the exception of the bias powerlevel. In the step of block 1730 of FIG. 17, the power level of the biaspower generator 125 of FIG. 11 is set at the beginning of apredetermined range. The measurement instrument 140 then senses thevoltage current and power at the impedance match 130 in order to measurewafer voltage, ion density and etch rate in the manner describedpreviously with respect to FIGS. 1-8 (block 1740 of FIG. 17). Thesemeasurements are sent to the contour generator 1120 and stored in amemory 1120 a. In the next step (block 1750 of FIG. 17), the power levelof the bias power generator 125 of FIG. 11 is incremented (by command ofthe controller 1110) to a slightly higher value and held at that value.A determination is then made in the step of block 1760 of FIG. 17 as towhether or not the latest bias power level is at the end of the biaspower range. If not (ANO@ branch of block 1760), the operation returnsin a loop 1765 to the step of block 1740. The steps within the loop 1765are repeated in this manner until the end of the bias power range isreached (AYES@ branch of block 1760). The result is that three sets ofdata corresponding to functions of bias power defining the behaviors ofwafer voltage, ion density and etch rate are stored in the memory 1120a. Using conventional data fit algorithms, the contour generator usesthe three sets of data to produce algebraic functions corresponding tothe data, which are stored in the memory 1120 a as follows:V_(wafer) = f_(a)(P_(bias))_(i) = f_(b)(P_(bias))_(i)ER = f_(c)(P_(bias))_(i)where η is plasma ion density, ER is etch rate and the index i refers tothe current level of the source power generator 915 (block 1770). In thenext step of FIG. 17 (block 1780), the level of the source powergenerator 915 is incremented to a new value so that i6i+1. If the newsource power level is not at the end of the source power range (ANO@branch of block 1790), then the operation returns in a loop 1795 to thestep of block 1730, and the steps within the loop 1795 (i.e., blocks1730 through 1790) are repeated until the source power level reaches theend of the source power range (AYES@ branch of block 1790). The resultis that many sets of the functionsV_(wafer) = f_(a)(P_(bias))_(i) = f_(b)(P_(bias))_(i)ER = f_(c)(P_(bias))_(i)for all values of i within the source power range are stored in thememory 1120 a. This permits an analytical determination of whether ornot the behavior of the three behavior parameters V_(wafer), η, ER withbias power changes with source power. I have discovered that it does notchange to a great extent, so that bias power and source power are atleast nearly independent variables. Thus, a single function of biaspower for each of the parameters V_(wafer), η, ER generally suffices asa fairly accurate prediction of behavior over the entire range of thesource power level, at least for the range chosen in the workingexamples given later in this specification. Thus, the loop 1795 of FIG.17 may not be strictly necessary. Instead, it may be acceptable tochoose a single value for the source power level in the middle of thesource power level range in step 1720 and perform the loop of 1765 toproduce a single set of data for each of the three functionsV_(wafer) = f_(a)(P_(bias))_(i) = f_(b)(P_(bias))_(i)ER = f_(c)(P_(bias))_(i)These three functions of bias power are stored in the memory 1120 a.

The operation depicted in FIG. 18 will now be described in detail withreference to both FIGS. 11 and 18. In the step of block 1810 of FIG. 18,the frequencies of the bias and source power generators 125, 920 of FIG.11 are set to constant values, the exhaust rate of a vacuum pump 1180 ofthe reactor of FIG. 11 is controlled to achieve a constant chamberpressure, and mass flow rates from gas supplies 1182, 1184 are setthrough a mass flow controller 1186 of FIG. 11 to constant values. Inthe step of block 1820 of FIG. 18, the power level of the bias powergenerator 125 of FIG. 11 is set to an initial set point, so that theentire process is at a steady state with the exception of the sourcepower level. In the step of block 1830 of FIG. 18, the power level ofthe source power generator 920 of FIG. 11 is set at the beginning of apredetermined range. The measurement instrument 140 then senses thevoltage current and power at the impedance match 130 in order to measurewafer voltage, ion density and etch rate in the manner describedpreviously with respect to FIGS. 1-8 (block 1840 of FIG. 18). Thesemeasurements are sent to the contour generator 1120 and stored in thememory 1120 a. In the next step (block 1850 of FIG. 18), the power levelof the source power generator 920 of FIG. 11 is incremented (by commandof the controller 1110) to a slightly higher value and held at thatvalue. A determination is then made in the step of block 1860 of FIG. 18as to whether or not the latest source power level is at the end of thesource power range. If not (NO branch of block 1860), the operationreturns in a loop 1865 to the step of block 1840. The steps within theloop 1865 are repeated in this manner until the end of the source powerrange is reached (YES branch of block 1860). The result is that threesets of data corresponding to functions of source power defining thebehaviors of wafer voltage, ion density and etch rate are stored in thememory 1120 a. Using conventional data fit algorithms, the contourgenerator 1120 uses the three sets of data to produce algebraicfunctions corresponding to the data, which are stored in the memory 1120a as follows: V_(wafer) = f_(a)(P_(bias))_(i) = f_(b)(P_(bias))_(i)ER = f_(c)(P_(bias))_(i)where η is plasma ion density, ER is etch rate and the index i refers tothe current level of the bias power generator 125 (block 1870). In thenext step of FIG. 18 (block 1880), the level of the bias power generator125 is incremented to a new value so that i6i+1. If the new bias powerlevel is not at the end of the bias power range (NO branch of block1890), then the operation returns in a loop 1895 to the step of block1830, and the steps within the loop 1895 (i.e., blocks 1830 through1890) are repeated until the bias power level reaches the end of thebias power range (YES branch of block 1890). The result is that manysets of the functionsV_(wafer) = f_(a)(P_(bias))_(i) = f_(b)(P_(bias))_(i)ER = f_(c)(P_(bias))_(i)for all values of i within the bias power range are stored in the memory1120 a. This permits an analytical determination of whether or not thebehavior of the three behavior parameters V_(wafer), η, ER with sourcechanges with bias power. I have discovered (as in the case of FIG. 17)that it does not change to a great extent, so that bias power and sourcepower are at least nearly independent variables, as discussed above.Thus, a single function of source power for each of the parametersV_(wafer), η, ER generally suffices as a fairly accurate prediction ofbehavior over the entire range of the bias power level, at least for therange chosen in the working examples given later in this specification.Thus, the loop 1895 of FIG. 18 may not be strictly necessary. Instead,it may be acceptable to choose a single value for the bias power levelin the middle of the bias power level range in step 1820 and perform theloop of 1865 to produce a single set of data for each of the threefunctions V_(wafer) = f_(a)(P_(bias))_(i) = f_(b)(P_(bias))_(i)ER = f_(c)(P_(bias))_(i)

These three functions of source power are stored in the memory 1120 a.Thus, upon completion of the operations of FIGS. 17 and 18, the memory1120 a holds the following pair of functions for the wafer voltage:V _(wafer) =f _(a)(P_(source))V _(wafer) =f _(a)(P_(bias))and following pair of functions for the ion density: = f_(b)(P_(source)) = f_(b)(P_(bias))and the following pair of functions for etch rate:ER=f _(c)(P_(source))ER=f _(c)(P_(bias)).

In the operation illustrated in FIG. 19, the contour generator 1120combines each pair of functions having a single variable P_(source), orP_(bias), respectively, into a single combined function of the variablepair P_(source) and P_(bias.) This produces the following threefunctions:V _(wafer)(P _(source) , P _(bias))η(P _(source) , P _(bias))ER(P _(source) , P _(bias)).

Contours of constant parameter values (e.g., a contour of constant wafervoltage, a contour of constant etch rate, a contour of constant iondensity) are found by setting the respective function to a constantvalue and then solving for P_(source) as a function of P_(bias). Forexample, in order to generate a contour of constant wafer voltage at 300V, the function V_(wafer)(P_(source), P_(bias)) is set equal to 300 V,and then solved for P_(source.)

Operation of the contour generator 1120 of FIG. 11 in carrying out theforegoing steps of generating the combined two-variable functions andthen solving them for P_(source) as a function of P_(bias) at variousconstant values is illustrated in FIG. 19. Referring now to FIG. 19, thefirst step (block 1910) is to take the single variable functions ofwafer voltage, i.e., V_(wafer)(P_(source)) and V_(wafer)(P_(bias)) andfind their combined function. The next step (block 1920) is to take thesingle variable functions of ion density, i.e., η(P_(source)) andη(P_(bias)) and find their combined function η(P_(source), P_(bias)).The third step (block 1930) is to take the single variable functions ofetch rate, i.e., ER(P_(source)) and ER(P_(bias)) and find their combinedfunction ER(P_(source), P_(bias)).

Then, the contours of constant values are generated. To generate acontour of constant wafer voltage (block 1940 of FIG. 19), the functionV_(wafer)(P_(source), P_(bias)) is set equal to a constant value ofwafer voltage and the resulting expression is then solved for P_(source)as a function of P_(bias.) This step is repeated for a range of constantwafer voltage values to generate a set of contours covering the range.These contours are stored in the memory 1120 a of FIG. 11 (block 1945 ofFIG. 19).

To generate a contour of constant ion density (block 1950 of FIG. 19),the function η(P_(source), P_(bias)) is set equal to a constant value ofion density and the resulting expression is solved for P_(source) as afunction of P_(bias). This step is repeated for a range of constant iondensity values to generate a set of contours covering the range of iondensity values. These contours are stored in the memory 1120 a of FIG.11 (block 1955 of FIG. 19).

To generate a contour of constant etch rate (block 1960 of FIG. 19), thefunction ER(P_(source), P _(bias)) is set equal to a constant value ofetch rate and the resulting expression solved for P_(source) as afunction of P_(bias.) This step is repeated for a range of constant etchrate values to generate a set of contours covering the range of etchrate values. These contours are stored in the memory 1120 a of FIG. 11(block 1965 of FIG. 19).

Generally, each combined two-variable function, e.g.,V_(wafer)(P_(source), P_(bias))) can be approximated by the product ofthe pair of individual functions, e.g., V_(wafer)(P_(source)) andV_(wafer)(P_(bias)). For example, ignoring all control parameters exceptRF power level and ignoring constants of proportionality:V _(wafer) =f _(a)(P _(source))·[P _(source)]^(1/2)V _(wafer) =f _(a)(P _(bias))·[P _(bias)]^(1/2)so that the combined two-variable function is approximately:V_(wafer)=F_(a)(P_(source),P_(bias))=f_(a)(P_(source))f_(a)(P_(bias))·[P_(source)]^(1/2)[P_(bias)]^(1/2)This expression, however is not exact. The exact function is best foundby curve-fitting techniques involving all control parameters, namelyP_(source) and P_(bias), as above, and in addition, source powerfrequency, bias power frequency, chamber pressure, and magnetic field(if any). I have found the following expression for V_(wafer) as afunction of both P_(source) and P_(bias:)V _(wafer)(P _(source) , P _(bias))=V _(O)(P _(bias) /P _(bO))^(0.4)[(P_(source) /P _(sO))K ₁(p/p _(O))⁻¹+(p/p _(O))^(0.5)]^(−0.5)where P_(bO) is a maximum bias power value, P_(sO) is a maximum sourcepower value, p_(O) is a minimum chamber pressure, and p is the actualchamber pressure. In the reactor chamber described above, the maximumsource power P_(sO) was 1500 Watts, the maximum bias power P_(bO) was4500 Watts and the minimum pressure p_(O) was 30 mT. These values maydiffer from the foregoing example depending upon chamber design andprocess design. V_(O) is determined in accordance with the followingprocedure: the maximum bias power P_(bO) is applied to the waferpedestal while the source power is held to zero and the chamber is heldto the minimum pressure p_(O). The wafer voltage V_(wafer) is thenmeasured and this measured value is stored as V_(O). K₁ is thendetermined by increasing the source power to its maximum value P_(sO)and then measuring the wafer voltage V_(wafer) again, and K₁ is adjusteduntil the foregoing equation yields the correct value for V_(wafer).

The exponents in the foregoing equations were obtained by an extensivetrial and error parameterization process for the reactor described inthis specification. These exponents may be useful for other reactordesigns, or the user may wish to try other exponents, depending upon theparticular reactor design.

Ion density, η, and etch rate, ER, are both functions of V_(wafer) andb, the plasma susceptance or imaginary part of the plasma admittance, asdescribed previously herein with reference to FIG. 8:  = b²V_(wafer)²and ER = kb²V_(wafer)^(3/2)

Therefore, only the plasma susceptance b need be specified in additionto V_(wafer) to define ER and η, for the sake of brevity. I have foundthe following expression for the plasma susceptance b as a function ofboth P_(source) and P_(bias:)b(P _(source) , P _(bias))=b _(O)(P _(bias) /P _(bO))^(−0.25)[(P_(source) /P _(sO))(p/p _(O))^(−0.65)][K ₂(P _(bias) /P_(bO))^(−0.62)(p/p _(O))³+(p/p _(O))^(0.27)]where the definitions above apply and in addition b_(O) is a referencesusceptance value. The reference susceptance value b_(O) is determinedin accordance with the following procedure: the maximum bias powerP_(bO) is applied to the wafer pedestal while the source power is heldto zero and the chamber is held to the minimum pressure p_(O). Thesusceptance b is then measured at the wafer support pedestal (using aV/I meter, for example) and this measured value is stored as b_(O). K₂is then determined by increasing the source power to its maximum valueP_(sO) and then measuring the susceptance b again, and K₂ is adjusteduntil the foregoing equation yields the correct value for b.

Ion density, η, and etch rate, ER, are then obtained by substituting theexpressions for V_(wafer) and b into the foregoing expressions for η andER.

The results of the contour generator operation of FIG. 19 areillustrated for various chamber pressures in FIGS. 20-26. FIG. 20illustrates contours of constant wafer voltage, contours of constant iondensity and contours of constant etch rate superimposed upon one anotherin P_(source)-P_(bias) space. The chamber pressure for these contourswas 100 mT. The contours of constant wafer voltage are depicted in solidlines. The contours of constant ion density are depicted in dashedlines. The contours of constant etch rate are depicted in dotted lines.The source power range (the vertical axis or ordinate) has a range fromzero to 1200 Watts. The bias power range (the horizontal axis orabscissa) has a range from 200 Watts to 1200 Watts. The stated values ofconstant wafer voltage are RMS volts. The stated values of constant iondensity are 10¹⁰ ions/cm³.

FIGS. 20, 21, 22, 23, 24 and 25 correspond to FIG. 20 for respectivechamber pressures of 100 mT, 30 mT, 70 mT, 150 mT, 200 mT and 250 mT,respectively.

Once a complete set of contours of constant voltage, constant etch rateand constant ion density have been generated and permanently stored inthe memory 120 a, the contour generator and even the measurementinstrument may be discarded. In such an implementation, the process setpoint controller 1110 would control the entire process based upon thecontours stored in the memory 120 a in response to user inputs. In thiscase, the process set point controller 1110 could apply the bias andsource power level commands directly to the bias and source powergenerators 125, 920, respectively, so that the feedback controller 950could also be eliminated in such an embodiment.

While the measurement instrument 140 has been described with referenceto discrete processors 310, 320, 340, 350, 360 that carry out individualcomputations, these processors comprising the measurement instrument 140can be implemented together in a programmed computer, such as aworkstation or a personal computer rather than as separate hardwareentities. The contour generator 1120 may also be implemented in aprogrammed computer or workstation. In addition, the feedback controller950 of FIG. 9 or FIG. 10 may be implemented in a programmed computer.Moreover, the process set point controller may be implemented in aprogrammed computer.

The measurement instrument 140 has been described in certainapplications, such as in a process control system. It is also useful asa tool for “fingerprinting” or characterizing a particular plasmareactor by observing the etch rate, ion density and wafer voltagemeasured by the instrument 140 at a selected process setting of sourcepower, bias power, pressure and other parameters.

While the description of FIG. 8 concerned an implementation in whichetch rate is computed as ER=b² V_(wafer) ² and ion density as η=kb²V_(wafer) ^(3/2), other functions may be employed, such as, for example,[bV_(wafer)]¹, or [bV_(wafer)]², or gV_(wafer) ^(3/2) (where g in thislast expression is the conductance defined previously in thisspecification).

While the invention has been described in detail with reference topreferred embodiments, it is understood that variations andmodifications thereof may be made without departing from the true spiritand scope of the invention.

1. A method of processing a workpiece on a workpiece support pedestal ina plasma reactor chamber in accordance with user-selected values ofplural plasma parameters of a group comprising ion density, wafervoltage, etch rate, wafer current, by controlling the chamber parametersof source power and bias power, said method comprising: a. for each oneof said plural plasma parameters, fetching from a memory a relevantsurface of constant value corresponding to the user-selected value ofsaid one plasma parameter, said surface being defined in a space ofwhich each of said chamber parameters is a dimension, and determining anintersection of the relevant surfaces, said intersection correspondingto a target value of source power and bias power; and b. setting saidsource power and bias power, respectively, to the target values.
 2. Themethod of claim 1 wherein said memory is provided as a component of saidreactor chamber, said method further comprising the initial step ofstoring in said memory a set of surfaces of constant value for each ofsaid plasma parameters, said set of surfaces corresponding to a set ofconstant values spanning a predetermined value range of thecorresponding plasma parameter.
 3. The method of claim 1 wherein thenumber of said plural plasma parameters is two.
 4. The method of claim 3wherein said plural plasma parameters are wafer voltage and one of iondensity and etch rate.
 5. The method of claim 1 further comprising:subsequently controlling plasma bias power by sensing a differencebetween the user-selected value of wafer voltage and a measured value ofwafer voltage and changing the plasma bias power to reduce saiddifference.
 6. The method of claim 5 further comprising: subsequentlycontrolling plasma source power by sensing a difference between theuser-selected value of plasma ion density or etch rate and a measuredvalue of plasma ion density or etch rate and changing the plasma sourcepower to reduce said difference.
 7. The method of claim 6 furthercomprising obtaining said measured values of wafer voltage and plasmaion density by the steps of: sampling values of RF electrical parametersat an input end of a transmission line coupling RF bias power to anelectrode within said wafer support pedestal, said electrode beingconnected to an output end of the transmission line; computing saidmeasured value of wafer voltage from the sampled values of the RFelectrical parameters; and computing said measured value of plasma iondensity or etch rate from the sampled values of the RF electricalparameters.
 8. The method of claim 7 wherein said RF electricalparameters comprise an input impedance, an input current and an inputvoltage.
 9. The method of claim 8 wherein the step of computingcomprises: computing a junction admittance of a junction between saidtransmission line and said electrode within the wafer pedestal from saidinput impedance, input current and input voltage and from parameters ofthe transmission line; providing shunt electrical quantities of a shuntcapacitance between the electrode and a ground plane; providing loadelectrical quantities of a load capacitance between the electrode and awafer on the pedestal; and computing said etch rate, plasma ion densityand wafer voltage from said junction admittance, said shunt electricalquantities, said load electrical quantities and a frequency of RF biaspower applied to said electrode.
 10. The method of claim 9 wherein saidparameters of said transmission line comprise a length of saidtransmission line, a characteristic impedance of said transmission lineand a complex loss factor of said transmission line.
 11. The method ofclaim 10 wherein: said shunt electrical quantities are computed from thesize of an electrode-to-ground gap length, an area of said wafer, anelectrode-to-ground dielectric constant and an electrode-to-groundconductive loss component; said load electrical quantities are computedfrom an electrode-to-wafer gap length, an area of the wafer, anelectrode-to-wafer dielectric constant and an electrode-to-waferconductive loss component.
 12. The method of claim 11 wherein the stepof computing said etch rate, plasma ion density and wafer voltagecomprises: first computing said wafer voltage and an imaginary part of aplasma admittance comprising a plasma susceptance, and computing saidion density and etch rate from said wafer voltage and said plasmasusceptance in said chamber, respectively, along said line.